Animated tentacle collision / Rigid body not working
Since you're animating them, they don't respond to physics, as earlier mentioned by Mutant Bob.

If you're looking for live animations, separate the tentacles so they can collide with each other. But if you use predetermined animations, this can glitch out on you. 

To prevent each tentacle to collide with itself, you have to tweak the settings a bit to increase stiffness and apply self colliding.